Luis is 9 years older than Ashley. Ten years ago, Luis was 4 times as old as Ashley. How old is Ashley now?
Answer: We can use the given information to write down two equations that describe the ages of Luis and Ashley. Let Luis's current age be $l$ and Ashley's current age be $a$ The information in the first sentence can be expressed in the following equation: $l = a + 9$ Ten years ago, Luis was $l - 10$ years old, and Ashley was $a - 10$ years old. The information in the second sentence can be expressed in the following equation: $l - 10 = 4(a - 10)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $a$ , it might be easiest to use our first equation for $l$ and substitute it into our second equation. Our first equation is: $l = a + 9$ . Substituting this into our second equation, we get the equation: $(a + 9)$ $-$ $10 = 4(a - 10)$ which combines the information about $a$ from both of our original equations. Simplifying both sides of this equation, we get: $a - 1 = 4 a - 40$ Solving for $a$ , we get: $3 a = 39$ $a = 13$.